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Applied Mathematical Analysis of Fluid Mechanics

Research Project

Project/Area Number 11640215
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionMeiji University

Principal Investigator

MORIMOTO Hiroko  School of Science and Technology, Meiji University, Professor, 理工学部, 教授 (50061974)

Co-Investigator(Kenkyū-buntansha) FUJITA Hiroshi  Research Institute of Educational Development, Tokai University, Professor, 教育開発研究所, 教授 (80011427)
KATURADA Masashi  School of Science and Technology, Meiji University, Associate Professor, 理工学部, 助教授 (80224484)
KONNO Reiji  School of Science and Technology, Meiji University, Professor, 理工学部, 教授 (20061921)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1999: ¥1,400,000 (Direct Cost: ¥1,400,000)
KeywordsNavier-Stokes equations / Boussinesq equations / Stationary solution / General outflow condition / ブシネスク方程式
Research Abstract

The problem to find a solution to the Navier-Stokes equations under the general outflow condition is unsolved problem for the domain having multiply connected boundary. It was known for small Reynolds number or under stringent outflow condition. In 1996, H.Morimoto and S.Ukai obtained some results for 2-dimensional annular domain. In 1997, H.Fujita and H.Morimoto studied the n-dimensional domain case with the boundary value which is gradient of a harmonic function and found the existence of solution even for large Reynolds number with some exceptional case, After that, in 1998, for 2-dimensionl symmetric domain, H.Fujita obtained the solenoidal extension of the symmetric boundary value satisfying Leray type inequality and succeeded to obtain an a priori estimate for solutions of Navier-Stokes equations, which proves the existence of solutions. The result was already shown by Ch.Amich in 1984, but the method of Fujita is more practical and useful and is on the way used for stringent outflow condition case. Applying this method for 2-dimensional infinite symmetric channel under general outflow condition, we obtained the follwings. For semi-infinte channel, V shaped channel and Y shaped channel, symmetric and having some finite boundary components, it is shown the existence of a solution satisfying the boundary condition and tending to Poiseuille flows in the infity if the Poiseulle flow is not so strong.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (21 results)

All Other

All Publications (21 results)

  • [Publications] N.Ishimura-H.Morimoto: "Remarks on the bolow-up criterion for 3D Boussinesq equations"MAS 9. 9. 1323-1332 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Morimoto-H.Fujita: "A remarks on the existence of steady Navier-Stokes flowa in 2D semi-infinite channel involving the general outflow condition"Mathematica Bohemica. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Morimoto-H.Fujita: "Stationary Navier-Stokes flow in 2dimensional Y-shaped channel under general outflow condition"Navier-Stokes Equations. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Morimoto-H.Fujita: "Stationary Navier-Stokes flow in 2-dimensional V-shaped infinite channel under general outflow condition"Topics in Mathematical Fluid Dynamics. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Fujita: "Non-stationary Stokes flow under leak boundary condition of friction type"Journal of Computing Mathematics. 19. 1-8 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] N.Saito-H.Fujita: "Remarks on traces of H -functions defined in a with corners"Journal of Mathematical Sciences, The University of Tokyo. 7. 325-345 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] N.Ishimura and H.Morimoto: "Remarks on the blow-up criterion for 3D Boussinesq equations"M^3AS. 9 (9). 1323-1332 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Morimoto and H.Fujita: "On Stationary Navier-Stokes Flows in 2D Semi-Infinite Channel Involving the General Outflow Condition"Ann.Univ.Ferrara, Sez.Vii, Sc.Mat.. Vol.XLVI. 285-290 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Morimoto and H.Fujita: "A remark on the existence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition"Mathematica Bohemica. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Morimoto and H.Fujita: "Stationary Navier-Stokes flow in 2-dimensional Y-shaped channel under general outflow condition""Navier-Styokes Equations : Theorey and Numerical Methods" Ed.Rodolfo Salvi, Marcel Decker. (to appera).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Morimoto and H.Fujita: "Stationary Navier-Stokes flow in 2-dimensional V-shaped infinite channel under general outflow condition""Topics in Mathmatical Fluid Dynamics" Ed. Remigio Russo, Quaderni di Matematica. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Fujita: "Non-stationary Stokes flow under leak boundary condition of friction type"Journal of Computing Mathematics. Vol.19 No.1. 1-8 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] N.Saito and H.Fujita: "Remarks on traces of H^1-functions defined in a domain with corners"Journal of Mathematical Sciences, The University of Tokyo. Vol.7. 325-345 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Morimoto,H.Fujita: "A remark on the exstence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition"Mathematica Bohemica. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Morimoto,H.Fujita: "Stationary Navier-Stokes flowin 2-dimensional Y-shaped channel under general outflow condition"Navier-Stokes Equations : Theory and Numerical Methods. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Morimoto,H.Fujita: "Stationary Navier-Stokes flow in 2-dimensional V-shaped infinite channel under general outflow condition"Topics in Mathematical Fluid Dynamics. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Fujita: "Non-stationary Stokes flows under leak boundary conditions of friction type"Journal of Computing Mathematics. 19. 1-8 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] N.Ishimura-H.Morimoto: "Remarks on the blow-up criterion for 3D Boussinesq equations"M^3AS. 9-9. 1323-1332 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] R.Konno: "A remark on the Schrodinger-type equation on manifolds, I"明治大学科学技術研究所紀要. 38. 25-32 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] R.Konno: "A remark on the Schrodinger-type equation on manifolds, II"明治大学理工学部研究報告. to appear.

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Kaneko-H.Fujita: "On Uzawa 's algorithm applied to Stokes flow under boundary condition of friction type"明治大学科学技術研究所紀要. 37. 239-258 (1998)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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